Superconducting photon detectors have emerged as a powerful new option for detecting single photons. System detection efficiency that incorporates the quantum efficiency of the device and system losses is one of the most important single-photon detector performance metrics for quantum information applications. Superconducting transition-edge sensors (TESs) are microcalorimeters that have the ability of distinguishing single photons with negligible dark counts. In addition, TESs are capable of directly measuring the photon number in a pulse of light. We have achieved near-unity system detection efficiency with TESs at particular wavelengths in the near-infrared by using multilayer structures that enhance the absorption of light into the active device material. We describe the design of the multilayer structure enabling high detection efficiency TESs including issues and requirements for obtaining detection efficiency values higher than 99 %. We describe the device fabrication and finally, show recent results of devices optimized for high detection efficiency using the multilayer structure.